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This paper provides a methodology to assist a strategic producer in making informed decisions on generation investment. A single target year is considered with demand variations modeled through blocks. The strategic behavior of the producer is represented through a bilevel model: the upper-level considers both investment decisions and strategic production actions and the lower-level corresponds to market clearing. Prices are obtained as dual variables of power balance equations. Rival uncertainties (on offering and investment) are characterized through scenarios. The resulting model is a large-scale mixed-integer LP problem solvable using currently available branch-and-cut techniques. Results pertaining to an illustrative example and a case study are reported and discussed. [ABSTRACT FROM PUBLISHER]

Purpose - The purpose of this paper is to develop a quantitative methodology for benchmarking process which is simple, effective and efficient as a rejoinder to benchmarking detractors who debate benchmarking is just a catch-up process. Design/methodology/approach - The methodology developed for benchmarking here consists of three phases; define, analyze and results. Define phase concentrates on what to benchmark, whereas analyze and results concentrate on how to benchmark. Analyze phase is developed based on two popular mathematical programming techniques which are called technique for order preference by similarity to ideal solution (TOPSIS) and goal programming. Findings - The developed benchmarking methodology is deployed in the case of business schools and results show its efficiency and effectiveness as well as its applicability to various business environments in implementation. Research limitations/implications - The main limitation here is necessity of collecting data about all the peers involved in benchmarking which indirectly restricts the number of peers in the benchmarking process. Practical implications - Based on the TOPSIS that addresses the benchmark (what to benchmark) and the GP model that addresses the way to reach the benchmark, this methodology may be implemented as a solution procedure for business benchmarking process. Originality/value - The novelty in this approach is that TOPSIS and GP are being used as a benchmarking techniques in a simple methodology which choose a non-real benchmark that is more than all the peers involved. In that sense, this research work may be the first, where quantitative methodology for benchmarking is developed and rejoined to the benchmarking old criticize that debates benchmarking is just a catch-up play. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of parts scheduling in a cellular manufacturing system (CMS) by considering exceptional parts processed on machines located in multiple cells. To optimize the scheduling of parts as well as to minimize material handling between cells, the practice has to develop processing sequences for the parts in cells. A commonly chosen objective is to find part sequences within cells which results in a minimum tardiness. This paper proposes a nonlinear mathematical programming model of the problem by minimizing the total weighted tardiness in a CMS. To solve the mathematical model, a scatter search approach is developed, in which the common components of scatter search are redefined and redesigned so as to better fit the problem. This scatter search approach considers two different methods to generate diverse initial solutions and two improvement methods, and adopts the roulette wheel selection in the combination method to further expand the conceptual framework and implementation of the scatter search. The proposed approach is compared with the commercial solver CPLEX on a set of test problems, some of which are large dimensions. Computational results have demonstrated the effectiveness of this scatter search approach. [ABSTRACT FROM AUTHOR]

Purpose -- Effective inventory management is very critical to market success. The purpose of this paper is to formulate an integrated model for the location of warehouse, the allocation of retailers to the opened warehouses, and finding the perfect policy for inventory control to managing order quantity and safety stock level. The goal is to select the optimum numbers, locations, capacities of the opening warehouses and inventory policy so that all stochastic customer demands can be satisfied. Design/methodology/approach -- It is assumed that the location of plant has already been determined and the paper answers the following questions: what are the location decisions over the planning horizon? How retailers are allocated to the warehouses? What are the optimum capacities for the opened warehouses? What is the best inventory policy for this supply chain? What are the total minimum costs? Findings -- The model was developed as a non-linear mixed integer programming and solved using Lagrange relaxation and sub-gradient search for the location/allocation module and a procedure for the capacity planning module. The results for the randomly selected problems show that the average duality gap ranges are between 0.51 and 1.58 percent. Also, from the CPU time point of view, the performance of the proposed algorithm was very good. Originality/value -- The paper addresses an integrated location, allocation, and inventory decisions in the design of a supply chain distribution network. In addition sensitivity analyses are conducted to evaluate the effects of the multi-capacity levels on some performance measures. [ABSTRACT FROM AUTHOR]

In this paper, we build on and extend Gartner and Kolisch (2014)'s hospital-wide patient scheduling problem. Their contribution margin maximising model decides on the patients' discharge date and therefore the length of stay. Decisions such as the allocation of scarce hospital resources along the clinical pathways are taken. Our extensions which are modeled as a mathematical program include admission decisions and flexible patient-to-specialty assignments to account for multi-morbid patients. Another flexibility extension is that one out of multiple surgical teams can be assigned to each patient. Furthermore, we consider overtime availability of human resources such as residents and nurses. Finally, we include these extensions in the rolling-horizon approach and account for lognormal distributed recovery times and remaining resource capacity for elective patients. Our computational study on real-world instances reveals that, if overtime flexibility is allowed, up to 5% increase in contribution margin can be achieved by reducing length of stay by up to 30%. At the same time, allowing for overtime can reduce waiting times by up to 33%. Our model can be applied in and generalised towards other patient scheduling problems, for example in cancer care where patients may follow defined cancer pathways. [ABSTRACT FROM AUTHOR]

Cut-off grade classifies the available supply of ore (valuable) and waste material within a mineralised deposit. Given the mining, processing and refining limitations of a mining operation, an optimal cut-off grade policy ensures that the flow of ore from the mine to the processing and refining facilities is maintained at the maximum possible throughput. This policy defines a schedule of cut-off grades along with corresponding quantities of mineralised material to be mined, processed and metal refined in each period of the scheduling horizon. The criteria that controls the development of cut-off grade policy aligns with the strategic objectives of an operation in order to maximise the discounted value (net present value or NPV) over the life of operation. This paper proposes a new mixed integer linear programming (MILP) based model that maximises NPV subject to the mining, processing, refining capacity constraints and develops an optimal cut-off grade policy for an open pit mining operation with multiple processing streams. An implementation of the proposed method on hypothetical and realistic data promises a relatively higher NPV as compared to the traditional Lane's approach practiced in the mining industry. [ABSTRACT FROM AUTHOR]

This paper proposes a novel mathematical model to solve the static and multistage transmission network expansion planning problems considering the optimal placement of series capacitive compensation (SCC) devices. This model jointly examines the construction of new transmission lines, transformers, and the optimal placement of SCC devices to minimize the total investment cost while satisfying the demand requirements in the planning horizon. The problem is formulated as a mixed-integer nonlinear programming problem, which is solved using a high-performance hybrid genetic algorithm. Simulations done in four electrical systems (IEEE 24-bus, South Brazilian 46-bus, North-Northeast Brazilian 87-bus, and Colombian 93-bus) show that inclusion of SCC devices in the planning model results in lower investment cost and a better redistribution of power flows through transmission components. [ABSTRACT FROM AUTHOR]

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In the traditional fuzzy matrix game, given a pair of strategies, the payoffs of one player are usually associated with themselves, but not linked to the payoffs of the other player. Such payoffs can be called self-evaluated payoffs. However, according to the regret theory, the decision makers may care more about what they might get than what they get. Therefore, one player in a matrix game may pay more attention to the payoffs of the other player than his/her payoffs. In this paper, motivated by the pairwise comparison matrix, we allow the players to compare their payoffs and the other ones to provide their relative payoffs, which can be called the cross-evaluated payoffs. Moreover, the players' preference about the cross-evaluated payoffs is usually distributed asymmetrically according to the law of diminishing utility. Then, the cross-evaluated payoffs of players can be expressed by using the asymmetrically distributed information, i.e., the interval-valued intuitionistic multiplicative number. Comparison laws are developed to compare the cross-evaluated payoffs of different players, and aggregation operators are introduced to obtain the expected cross-evaluated payoffs of players. Based on minimax and maximin principles, several mathematical programming models are established to obtain the solution of a matrix game with cross-evaluated payoffs. It is proved that the solution of a matrix game with cross-evaluated payoffs can be obtained by solving a pair of primal–dual linear-programming models and can avoid some unreasonable results. Two examples are finally given to illustrate that the proposed method is based on the cross-evaluated payoffs of players, and can directly provide the priority degree that one player is preferred to the other player in winning the game. [ABSTRACT FROM AUTHOR]

Transient traffic spikes are becoming a crucial challenge for network operators from both user-experience and network-maintenance perspectives. Different from long-term traffic growth, the bursty nature of short-term traffic fluctuations makes it difficult to be provisioned effectively. Luckily, next-generation elastic optical networks (EONs) provide an economical way to deal with such short-term traffic fluctuations. In this paper, we go beyond conventional network reconfiguration approaches by proposing the novel lightpath-splitting scheme in EONs. In lightpath splitting, we introduce the concept of SplitPoints to describe how lightpath splitting is performed. Lightpaths traversing multiple nodes in the optical layer can be split into shorter ones by SplitPoints to serve more traffic demands by raising signal modulation levels of lightpaths accordingly. We formulate the problem into a mathematical optimization model and linearize it into an integer linear program (ILP). We solve the optimization model on a small network instance and design scalable heuristic algorithms based on greedy and simulated annealing approaches. Numerical results show the tradeoff between throughput gain and negative impacts like traffic interruptions. Especially, by selecting SplitPoints wisely, operators can achieve almost twice as much throughput as conventional schemes without lightpath splitting. [ABSTRACT FROM AUTHOR]

The usage process of electronic equipment is divided into the task preparing process and the actual combat process. Based on the historical data acquired in the task preparing process, the GM(1,1) model for grey predicted value is employed. And based on the predicted value, the grey programming model for the jamming target assignment of the electronic equipment in the actual combat is also set up. The simulation results show that the model in the paper is feasible, effective and suitable for the target assignment of the electronic equipment in the actual combat. [ABSTRACT FROM AUTHOR]

Given a set of spatial units, such as land parcels and grid cells, how to allocate subsets of it to activities of interest while satisfying certain criteria? Such a decision process is here called spatial allocation. Though many problems of spatial allocation share this generic construct, each may have a quite unique set of criteria and interpret even the same criteria in its own way. Such diversity makes it difficult to model spatial allocation problems in unambiguous terms that are amenable to algorithmic solution. This paper proposes a classification scheme for spatial properties that helps to address a variety of spatial properties in establishing spatial allocation criteria. The implication of the paper is that a number of spatial properties and spatial allocation criteria can be decomposed into a few kinds of primitive spatial properties and their relations. [ABSTRACT FROM AUTHOR]

This paper studies the single-hoist cyclic scheduling problem in electroplating systems with two extended features. One extension is that the products must visit some processing tanks more than once (multi-function tanks). Another is that more than one identical tank is used at some stages. These extensions are common in practical electroplating lines and can increase the lines' processing capacity. However, they make the hoist scheduling problem more complicated and little research has been done to optimize the hoist moves in such extended practical systems. In this paper, we develop a comprehensive mixed integer linear programming model to find optimal solutions to the single-hoist cyclic scheduling problem for electroplating lines with these extensions. Examples are given to demonstrate the effectiveness of the model in different types of problems. [ABSTRACT FROM AUTHOR]

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets. [ABSTRACT FROM AUTHOR]

SML is a modeling language for the structured modeling framework, which represents the semantics as well as the mathematical structure of a model. This paper uses an SML approach to improve the object based universal relation data model. By this approach, both the relational structure of a database and the objects in relations are automatically derived by the associated SML schema. The interpretation part of an SML schema allows users to easily learn the meanings of the data before performing universal relation queries; the queries are then computed by using the automatically derived objects. With a goal of making queries simpler, this paper presents theories, table naming conventions, a confirmation approach, and a unified example illustrating many different concepts. It helps lay the foundation for the eventual development of a remarkably easy user interface for ad hoc query in computer-based modeling systems. We are hopeful that the results may in the future contribute to real applications in databases as well as in management science/operations research. [ABSTRACT FROM AUTHOR]

This paper is a compendium of results--theoretical and computational--from a series of recent papers developing a new American option valuation technique based on linear programming (LP). Some further computational results are included for completeness. A proof of the basic analytical theorem is given, as is the analysis needed to solve the inverse problem of determining local (one-factor) volatility from market data. The ideas behind a fast accurate revised simplex method, whose performance is linear in time and space discretizations, are described and the practicalities of fitting the volatility smile are discussed. Numerical results are presented which show the LP valuation technique to be extremely fast--lattice speed with PDE accuracy. American options valued in the paper range from vanilla, through exotic with constant volatility, to exotic options fitting the volatility smile. [ABSTRACT FROM AUTHOR]

Material requirements planning (MRP) is a basic tool for performing detailed material planning function in the manufacture of component parts and their assembly into finished items. MRP's managerial objective is to provide 'the right part at the right time' to meet the schedules for completed products. However satisfying end customer demands faster with lower inventories implies smarter scheduling which must simultaneously reflect actual capacity conditions. Therefore, the need is to schedule both capacity and materials simultaneously. Since MRP does not consider the availability of capacity resources to schedule production, consequently the schedules so developed are usually capacity infeasible. This paper proposes a three-step procedure to develop capacity feasible material and production schedules in a finite capacity environment. In the first step, an LP model produces capacity feasible but lot size relaxed planned order releases for all end products and assembly components which are then fed into a MRP processor, where a bill of material (BOM) explosion process generates material plans. Finally, these material plans are introduced to another LP model which assures that capacity feasibility is again restored. The mathematical models developed consider restrictions on lot sizes as well as alternative production routings and overtime decisions. A numerical example also is provided and some future research directions are outlined. [ABSTRACT FROM AUTHOR]

Background: Supply chains are the networks linking sources of supply with demand points and composed of so-called actors, i.e., producers, distributors/wholesalers, retailers, and customers/consumers. As in every network, supply chains contain vertices and arcs, the former represented by factories and warehouses (including distribution centers). Such facilities cause long-term and expensive investments. As a result, decisions on location and number of them belong to the strategic level of management and require quantitative analysis. To do this, mathematical models of the Facility Location Problem (FLP) are constructed to allow an application of optimization methods. Methods: Mathematical optimization or programming is the selection of the best solution, with regard to some criterion, from a set of feasible alternatives. The fundamental of mathematical optimization is the formulation of mathematical models of analyzed problems. Mathematical models are composed of objective function, decision variables, constraints, and parameters. These components are presented and compared in the paper concerning FLP from a supply chain perspective. Results: The ten mathematical models of the FLP are presented, including the two original ones. The models are classified according to such features as facility type they concern, including the desirable, neutral, and undesirable ones. The models and their components are characterized. In addition, their applicability and elasticity are analyzed. Finally, the models are compared and discussed from the supply chain point of view. Conclusions: However, the FLP mathematical models are relatively similar; the most important element of them for supply chain appropriate representation is an objective function. It strongly influences the possible applicability of FLP models and their solutions, as well. The objective functions having broader applicability turned out to be the maximized number of supply/demand points covered by facilities and the minimized number of facilities necessary to cover supply/demand points. However, not to locate all allowed facilities (use all the location sites) or as many as supply/demand points, but an appropriate number of them, it is necessary to take into account facility fixed costs. Thus, when locating logistics facilities, the minimized total cost of serving supply/demand points is the most appropriate objective function. [ABSTRACT FROM AUTHOR]

The analysis of the principal-agent problem usually requires the classical first-order approach (FOA). However, the validity of the FOA makes restrictive assumptions on the problem under consideration such as the convexity of the distribution function condition. The main aim of this paper is to compute the optimal wages and characterize a closed form solution to the risk-neutral principal-agent problem with limited liability constraints. The development in this paper mainly invokes certain techniques in the semi-infinite programming rather than the FOA. [ABSTRACT FROM AUTHOR]

In this paper, a novel self-learning gene expression programming (GEP) methodology named SL-GEP is proposed to improve the search accuracy and efficiency of GEP. In contrast to the existing GEP variants, the proposed SL-GEP features a novel chromosome representation in which each chromosome is embedded with subfunctions that can be deployed to construct the final solution. As part of the chromosome, the subfunctions are self-learned or self-evolved by the proposed algorithm during the evolutionary search. By encompassing subfunctions or any partial solution as input arguments of another subfunction, the proposed SL-GEP facilitates the formation of sophisticated, higher-order, and constructive subfunctions that improve the accuracy and efficiency of the search. Further, a novel search mechanism based on differential evolution is proposed for the evolution of chromosomes in the SL-GEP. The proposed SL-GEP is simple, generic and has much fewer control parameters than the traditional GEP variants. The proposed SL-GEP is validated on 15 symbolic regression problems and six even-parity problems. Experimental results show that the proposed SL-GEP offers enhanced performances over several state-of-the-art algorithms in terms of accuracy and search efficiency. [ABSTRACT FROM PUBLISHER]

In this paper, we address the problem of infeasibility of systems defined by convex inequality constraints, where some or all of the variables are integer valued. In particular, we provide a polynomial time algorithm to identify a set of all constraints which may affect a feasibility status of the system after some perturbation of the right-hand sides. We establish several properties of the irreducible infeasible sets and infeasibility sets in the systems with integer variables, proving in particular that all irreducible infeasible sets and infeasibility sets are subsets of the set of constraints critical to feasibility. Furthermore, the well-known Bohnenblust-Karlin-Shapley Theorem, which requires that a system of convex inequality constraints must be defined over a compact convex set, is generalized to convex systems without the assumption on compactness of the convex region. Extension of the latter result to convex systems defined over the set of integers is also provided. [ABSTRACT FROM AUTHOR]

Statistical model checking of unbounded time properties is challenging, because it requires an algorithm to estimate the measure of paths satisfying an unbounded until property from samples of finite length paths. In this paper, we survey all proposed algorithms for this problem, and critically evaluate them. [ABSTRACT FROM AUTHOR]

In the last years, many areas in science, business, and engineering have experienced an enormous growth in the amount of data that they are required to analyze. In many cases, this analysis relies intimately on data visualization and, as a result, graph drawing has emerged as a new field of research. This paper addresses the challenge of drawing hierarchical graphs, which is one of the most widely used drawing standards. We introduce a new mathematical model to automatically represent a graph based on the alignment of long arcs, which we combine with the classic arc crossing minimization objective in hierarchical drawings. We complement our proposal with a heuristic algorithm that can obtain high-quality results in the short computational time required by graph drawing systems. Our algorithm joins two methodologies, tabu search and strategic oscillation (SOS), to perform a fast and effective exploration of the search space. We conduct extensive experimentation that integrates our new mathematical programming formulation and the SOS tabu search that targets large instances. Our statistical analysis confirms the effectiveness of this proposal. [ABSTRACT FROM AUTHOR]

This note demonstrates that Freeland's (1976) modification of Ruefli's (1971) Generalized Goal Decomposition model can generate nonoptimal solutions and shows how these difficulties can be corrected. In several papers on multi-level planning, it has been suggested that extending the hierarchical levels of the models from two to three or more levels is a straightforward process. This paper shows that this assertion is generally not true. The note points out that in Freeland's (1976) three-level model, the interactions between the two lowest levels of the hierarchy must be strictly controlled before information is passed to the highest level of the organization. [ABSTRACT FROM AUTHOR]

This paper focuses upon the maximization of labor productivity through selection of the optimal number, duration, and placement of rest breaks. It is demonstrated that resolution of the limited validity associated with previous models leads to a mixed-integer quadratic programming formulation of this problem. Efficient analytic procedures are developed which allow solutions to be obtained in minutes using a hand-held calculator. Then, the characteristics, properties, and potential effectiveness of optimal solutions are examined through an illustration from an existing work environment. Issues relevant to the implementation of the models are presented in a summary of an initial experiment in which one of the models in this paper was used to select rest break policy. The results of this experiment indicated that the output achieved using the model's policy was 13% higher than the output achieved when the subjects used their own rest break policies. Several future research topics are also identified. [ABSTRACT FROM AUTHOR]

This paper compares two approaches to the solution of weighted multiobjective linear programming problems: the fuzzy linear programming method and the minmax distance metric. The two models produce an identical solution for equally weighted objectives, but the solutions differ when the objectives are unequally weighted. This is due to the under-lying meaning of the weights attached to each solution method. The paper illustrates the graphical meaning of the weights and the implications to the decision maker. [ABSTRACT FROM AUTHOR]

The theory of geometric programming is concerned with the solution of certain nonlinear programming problems in which the objective function and the constraints are polynomial expressions with positive coefficients. The solution of the primal geometric programming problem can be obtained by solving the dual problem. In certain cases the solution to the dual problem, and hence the solution to the primal problem, is obtained immediately by solving the dual constraint system for the optimal dual vector. Such problems are said to possess "degree of difficulty zero." This paper describes a solution procedure for geometric programming. The procedure involves the formation of an augmented problem possessing degree of difficulty zero. The solution to the original problem requires the estimation of certain parameters in the augmented problem. An iterative procedure for estimating these parameters is described in this paper. According to the author, the solution procedure developed in this paper involves the formation of an augmented geometric program possessing a degree of difficulty equal to zero.

Estimating the annual production cost is a crucial component in long range capacity planning for electric utilities. Traditional simulation-based methods are quite expensive in terms of computer resources (space and time), while simpler mathematical programming-based models generally assume a linear variable production cost. This paper presents a method that incorporates quadratic production costs for each unit and uses optimization submodels to develop a system production cost versus output curve. The method is tested using data from a large southeastern utility. Production cost estimates within one percent of the estimates from a large simulation model were obtained with a small fraction of the simulation model's computing time. The concluding section discusses how the new method might be incorporated in procedures for capacity planning. [ABSTRACT FROM AUTHOR]

This paper considers optimization problems with a nonlinear-additive objective function and a single linear constraint. Such models have numerous direct applications and serve as subproblems in procedures for more complex problems. Some important portfolio selection problems can be expressed in this form, and the problem also arises in economic theory. Several authors have noticed independently that special cases and variants of the problem can be solved exactly by surprisingly simple, finite algorithms. The major purpose of this paper is to present these results in a unified framework, which then permits substantial generalizations and extensions. The results lend themselves to an appealing managerial interpretation, similar to the rate-of-return cutoff rules of capital budgeting. [ABSTRACT FROM AUTHOR]

Peleg established a fundamental theorem which says that convex effectivity functions are stable. He also proved its partial converse: Within the class of maximal effectivity functions, stability implies convexity. The present paper provides another partial converse: Within the class of α-effectivity functions derived from extensive game forms (without chance moves), stability implies convexity. It also provides a geometric characterization of the stability condition for the latter class. [ABSTRACT FROM AUTHOR]

The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In first step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, -constraint method is applied to find the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model. [ABSTRACT FROM AUTHOR]

This work presents a mathematical modelling based approach including many constraints encountered at Universities in Turkey. As in many other countries also in Turkey it appears that universities are too autonomous, and they have medley of individual requirements and constraints. This condition makes it very difficult to suggest a generalized model and a solution algorithm for university timetabling problem (UTP). In general, in this paper it is aimed to design compatible and flexible approach to generate timetable so as to meet all the requirements of Turkish universities. First, by reviewing the studies in which mathematical modelling approaches were used, comprehensive information about the subject has been presented. Then, proposed hierarchical mathematical modelling approach is described (HMMA). Since (UTP) is highly context-dependent the results of this study couldn't been compared to those of the studies which are published already. Proposed approach is tested 2015-2016 academic year winter term data of Atatürk University Engineering Faculty and obtained results are presented comparatively with results obtained from manual preparation in terms of seven objectives. [ABSTRACT FROM AUTHOR]

Strategic staff planning in consultancies is a major problem that directly affects the firm's performance and capacity for dealing with projects appropriately. Furthermore, the decisions taken now will have long term consequences, because consultants are highly qualified workers who need very long learning periods to achieve enough expertise. In other words, the size and composition of the future workforce depends on the decisions taken today. It is important to underline that the system anticipates future capacity adjustment in response to forecasted demand requirements; therefore, it is flexible to plan the workforce in different scenarios and time horizons. This paper proposes a decision support system based on a mathematical optimization model for solving strategic staff planning, taking the company's strategies, policies and objectives into account and optimizing both the costs and the staff composition. The tool is tested by applying it in an office belonging to a multinational consulting firm. [ABSTRACT FROM AUTHOR]

At the heart of van der Linden's approach to automated test assembly ( ATA) is a linear programming/integer programming ( LP/ IP) problem. A variety of IP solvers are available, ranging in cost from free to hundreds of thousands of dollars. In this paper, I compare several approaches to solving the underlying IP problem. These approaches range from traditional computer programming, through LP/ IP-specific modeling languages, to plug-ins for common software such as Excel. The features of several of the major IP solvers are briefly reviewed, describing which of the features are more or less useful in the context of ATA. The appendices include a list of resources that I have found particularly useful. [ABSTRACT FROM AUTHOR]

In this paper, a multi-product single machine scheduling problem with the possibility of producing defected jobs, is considered. We concern rework in the scheduling environment and propose a mixed-integer programming (MIP) model for the problem. Based on the philosophy of just-in-time production, minimization of the sum of earliness and tardiness costs is taken into account as the objective function. It is possible to obtain optimal solutions for small-sized problems using the MIP model by operation research solvers. Due to the complexity of the problem, exact algorithms are inefficient for medium and large-sized problems. For large-sized problems, an adapted genetic algorithm (GA) is used to solve them. The implemented GA is compared to the optimal solutions generated by an optimization solver, and to the solutions generated by dispatching rules procedure. Computational experiments are performed to illustrate the efficiency of the adapted GA algorithm. [ABSTRACT FROM AUTHOR]

The longest path problem (LPP) is to find a simple path with maximum length in a given graph, which plays an important role in many real-world applications, such as job shop scheduling problem, route planning. LPP in directed acyclic graphs (DAG) has important applications, such as finding the critical path in scheduling problems. In this paper, we present an amoeba algorithm, inspired by the plasmodium of Physarum polycephalum, to solve the longest path problem in the DAG. The proposed method is composed of two parts: (1) a fictional rule is constructed to replace ohm's law. Based on this mechanism, the current tends to pass through the conductor with more resistance. (2) The original amoeba model is adjusted to work in a special circuit based on our fictional rule. As a topological sorting is necessary in model calculations, it can only deal with LPP in DAG. In addition, the evolving processes of the proposed model have been introduced in detail in this paper. A numerical example is used to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The sphere is an undeveloped (unfolded) surface. The surface of the sphere can be developed by approximate methods. This paper presents a parallel calculus between the method of the spherical sector spindles and the method using MATHEMATICA program, for the flat unfold surface of the sphere. The general case is the sphere having radius "r" sectioned by "n" radial sectional plans. The specific case is presented for a three values of sphere radius: r = 25; 50 ; 100 mm and n = 12 radial sectional plans. [ABSTRACT FROM AUTHOR]

The optimum coupon schedule for serial bonds issued by municipalities has been solved as a knapsack problem, and is widely implemented in bank and nonbank underwriting firms. A large subset of issues carries the additional requirement that limits the number of distinct coupons which the underwriters may assign to the issue. The paper formulates this problem as a dynamic programming model and discusses the computational aspects relating to this formulation by comparing it with a direct 0/1 integer programming model. Some computational experience is also provided. [ABSTRACT FROM AUTHOR]

The bond portfolio problem is viewed as a multistage decision problem in which buy, sell, and hold decisions are made at successive (discrete) points in time. Normative models of this decision problem tend to become very large, particularly when its dynamic structure and the uncertainty of future interest rates and cash flows are incorporated in the model. In this paper we present a multiple period bond portfolio model and suggest a new approach for efficiently solving problems which are large enough to make use of as much information as portfolio managers can reasonably provide. The procedure utilizes the decomposition algorithm of mathematical programming and an efficient technique developed for solving subproblems of the overall portfolio model. The key to the procedure is the definition of subproblems which are easily solved via a simple recursive relationship. [ABSTRACT FROM AUTHOR]

This paper will present a model of equipment replacement in a stochastic environment utilizing a number of the component characteristics of an operations research orientation while being designed to emphasize the role of a stochastic representation of technological change and/or maintenance costs and the implications these have for the decision about replacement of equipment. The "replacement" referred to here is replacement of a machine in its entirety rather than the usual periodic-review-replacement-of-individual-pieces analysis to which the term "replacement" frequently refers in operations research literature. The paper outlines the approaches to equipment replacement in the literature of economics and the well-known Terborgh model and then introduces a stochastic model for studying certain aspects of equipment replacement together with the form of its analytic solution. A comparison of the cost implications of the Terborgh and stochastic model is presented for a specific example utilizing motor vehicle data. In addition, a general analytic comparison of the two replacement rules is provided. [ABSTRACT FROM AUTHOR]

This paper is concerned with characterizing decision rules for the sequential E-model of chance-constrained programming. A key feature of our characterization will be a detailed discussion of various interpretations of the probability operator in the chance constraints. Specifically we define two new classes of decision rules by exhibiting those sets of constraints which locally support the corresponding probability requirements. The question of how the probabilistic constraints for future periods are affected by previous decisions and realizations of the random variables is considered in detail. Since we are primarily concerned with the feasibility of decision rules, we deal mainly with the constraints of the model. The procedure for selecting the optimum rule from among a particular class of feasible rules depends on the objective function and is briefly discussed in the final section along with some implications concerning the form of the optimum rule. The application of our proposed rules to a two-period example previously appearing in the literature concludes the paper. [ABSTRACT FROM AUTHOR]

The paper focuses on multi-stage production systems. If such a system is of the more general type than a production line and many products have to be manufactured according to different technological sequence restrictions then two problems arise: (1) scheduling and (2) sequencing. The formulation of that problem requires the simultaneous consideration of the scheduling and sequencing aspect. The paper integrates these two functions into one single model using zero-one programming. [ABSTRACT FROM AUTHOR]

This paper establishes sufficient conditions for decision rules to be optimal for two n-period P-models of chance-constrained programming. The models considered are the triangular model with total probability constraints and the block triangular model with conditional probability constraints. It is shown that, for both these models, a sufficient condition for optimality is that the decision rule be the optimal piecewise linear rule. Proofs of theorems are based on results contained in earlier papers by the authors, on n-period E-models of chance-constrained programming. [ABSTRACT FROM AUTHOR]

An inter-temporal quadratic programming model for selecting portfolios of risky assets is formulated. The model's application to capital budgeting is discussed in considerable detail. This is followed by briefer discussions of its application in other areas. The paper develops a new and more efficient way of using simulation to calculate the variance-covariance elements required as input to Markowitz-type models; this new procedure makes no further demands on the decision maker than do other simulation models that have been suggested. The paper also shows how such models can be made inter-temporal. Finally, the paper analyses the potentials for extending such models to include other theoretical considerations that have been proposed in the literature. [ABSTRACT FROM AUTHOR]

This paper gives a detailed description of an algorithm for the solution of a specialized Linear Programming model, to be called the Machine Loading model. It is a generalization of the Transportation Problem, in that weighting factors are applied to the individual elements which form the row and column sums. For the Machine Loading model, the simplex method reduces to a specialized algorithm which generalizes the stepping stone method of the Transportation Problem [2], [3]. With the resulting generalized stepping stone method, it becomes practicable to solve many large-scale problems for which the direct application of the simplex method would be impracticable. The present paper is restricted to a discussion of the following topics: (I) the general characteristics of the model and its topological features; (ii) a detailed solution algorithm, including a consideration of degenerate cases and the use of a computer; (iii) a more restrictive capacitated model and the corresponding modifications to the solution algorithm; and (iv) the complete illustrative solution of a numerical example. The purpose is to aid interested readers in gaining familiarity with the algorithm and facility in the solution of numerical problems. No derivations or proofs will be included. [ABSTRACT FROM AUTHOR]

This paper is concerned with formulating, exploring and interpreting the uses and constructs which may be derived from a mathematical model of programming type which expresses more realistically than past efforts the actual conditions of current operations. It is an attempt to provide a means of attaining thereby an objective understanding of the implications of actual Federal Reserve liquidity policy on the actions and opportunities of banking institutions. The model presented corresponds to the problem of determining an optimal portfolio for an individual bank over several time periods in accordance with requirements laid down by bank examiners which are interpreted as defining limits within which the level of risk associated with the return on the portfolio is an acceptable one. The problem is transformed into an equivalent one offering advantages of analysis and of computation. Some methods of effective computation are explored. [ABSTRACT FROM AUTHOR]

The aim of this paper is building a mathematical model for Travelling salesman problem (TSP) with multi-objective; the model describes the problem of (TSP) with three objectives (cost, distance, time), Real data were collected with a sample of twenty states of United State of America, Three methods were used (Branch and Bound algorithm, Nearest neighbor and two-way exchange improvement heuristic), The comparison was conducted among results reached. To solve the problem multi-objective of (TSP), The weighted model demonstrated the effectiveness and flexibility to solve real problems of multi-objective (TSP), where it can be said that it is impossible to solve this problem without resorting to multiple -objective mathematical models, In other words, the number of possible rout for the 20 town is {(n -1)! =19! =121645100408832000}, to find the optimal routs among these routs it takes very long time and a lot of effort, here stand out importance of two-way exchange improvement heuristic algorithm, where this rout is satisfactory to the decision maker in terms of cost, distance and time. [ABSTRACT FROM AUTHOR]

In this paper, we address the non-permutation flowshop scheduling problem with minimal and maximal time lags between successive operations of each job. For this problem, the set of permutation schedules is not a dominant set but not all non-permutation schedules are feasible because they are not always able to satisfy all time lag constraints. We present a theoretical study, limited to the two-machine case, and related to the change on one machine of the order of two successive jobs of a permutation schedule. This study gives first the necessary conditions to make such move with regard to the feasibility of the schedule; secondly the necessary conditions to make such move interesting with regard to either the makespan or the number of tardy jobs. Through this analysis, we obtain new properties of dominance of permutation schedules. The results of the study are incorporated into a heuristic algorithm which starts the search with optimal permutation schedules and tries to improve them so as to obtain better non-permutation schedules. We also propose a mixed integer linear programming model. The objective function is to minimize lexicographically the number of tardy jobs as primary criterion and the makespan as secondary one. Computational experiments are performed to compare permutation with non-permutation schedules. [ABSTRACT FROM AUTHOR]

Analyzing the behavior and stability properties of a local optimum in an optimization problem, when small perturbations are added to the objective functions, are important considerations in optimization. The tilt stability of a local minimum in a scalar optimization problem is a well-studied concept in optimization which is a version of the Lipschitzian stability condition for a local minimum. In this paper, we define a new concept of stability pertinent to the study of multiobjective optimization problems. We prove that our new concept of stability is equivalent to tilt stability when scalar optimizations are available. We then use our new notions of stability to establish new necessary and sufficient conditions on when strict locally efficient solutions of a multiobjective optimization problem will have small changes when correspondingly small perturbations are added to the objective functions. [ABSTRACT FROM AUTHOR]